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<title>mpt_scale_matrix</title>
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<h1 class="reftitle">mpt_scale_matrix</h1>
<h2>Purpose</h2>
<p>Scales matrix row-wise and column-wise</p>
<h2>Syntax</h2>
<pre class="synopsis">[An,D1,D2] = mpt_scale_matrix(A)</pre>
<h2>Description</h2>
<p></p>
        Scales matrix <img src="../../../fig/mpt/utils/mpt_scale_matrix1.png" alt="../../../fig/mpt/utils/mpt_scale_matrix1.png"> by finding diagonal matrices <img src="../../../fig/mpt/utils/mpt_scale_matrix2.png" alt="../../../fig/mpt/utils/mpt_scale_matrix2.png"> and <img src="../../../fig/mpt/utils/mpt_scale_matrix3.png" alt="../../../fig/mpt/utils/mpt_scale_matrix3.png">
        in <img src="../../../fig/mpt/utils/mpt_scale_matrix4.png" alt="../../../fig/mpt/utils/mpt_scale_matrix4.png"> such that infinity
        norm of each row and column approaches 1.

        The problem is given as
        <p class="programlistingindent"><img src="../../../fig/mpt/utils/mpt_scale_matrix15.png" alt="../../../fig/mpt/utils/mpt_scale_matrix15.png"></p>
        
        Scaling matrix is used in solving linear equations of the type <img src="../../../fig/mpt/utils/mpt_scale_matrix5.png" alt="../../../fig/mpt/utils/mpt_scale_matrix5.png">
        for badly scaled matrix <img src="../../../fig/mpt/utils/mpt_scale_matrix6.png" alt="../../../fig/mpt/utils/mpt_scale_matrix6.png"> as follows:
        <p class="programlistingindent"><img src="../../../fig/mpt/utils/mpt_scale_matrix16.png" alt="../../../fig/mpt/utils/mpt_scale_matrix16.png"></p>
        First solve <img src="../../../fig/mpt/utils/mpt_scale_matrix7.png" alt="../../../fig/mpt/utils/mpt_scale_matrix7.png">, then obtain <img src="../../../fig/mpt/utils/mpt_scale_matrix8.png" alt="../../../fig/mpt/utils/mpt_scale_matrix8.png">.
        
	<h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>A</tt></td>
<td>
<p></p> Input matrix do be scaled. The matrix can be also rectangular. <p>
	    		Class: <tt>double</tt></p>
</td>
</tr></tbody>
</table>
<h2>Output Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody>
<tr valign="top">
<td><tt>An</tt></td>
<td>
<p></p> Scaled matrix <img src="../../../fig/mpt/utils/mpt_scale_matrix9.png" alt="../../../fig/mpt/utils/mpt_scale_matrix9.png"> such that <img src="../../../fig/mpt/utils/mpt_scale_matrix10.png" alt="../../../fig/mpt/utils/mpt_scale_matrix10.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>D1</tt></td>
<td>
<p></p> Diagonal matrix <img src="../../../fig/mpt/utils/mpt_scale_matrix11.png" alt="../../../fig/mpt/utils/mpt_scale_matrix11.png"> such that <img src="../../../fig/mpt/utils/mpt_scale_matrix12.png" alt="../../../fig/mpt/utils/mpt_scale_matrix12.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>D2</tt></td>
<td>
<p></p> Diagonal matrix <img src="../../../fig/mpt/utils/mpt_scale_matrix13.png" alt="../../../fig/mpt/utils/mpt_scale_matrix13.png"> such that <img src="../../../fig/mpt/utils/mpt_scale_matrix14.png" alt="../../../fig/mpt/utils/mpt_scale_matrix14.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
</tbody>
</table>
<h2>References</h2>
<p class="citetitle">[1] 
    Details of the method are in file drRAL2001034.ps.gz
</p>
<p class="citetitle">[2] 
      <tt>http://www.numerical.rl.ac.uk/reports/reports.html</tt>
   </p>
<h2>See Also</h2>
<a href="../mptopt.html">mptopt</a>, <a href="../modules/solvers/mpt_solve.html">mpt_solve</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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